The life of psychiatrist Elisabeth Targ was haunted by coincidences. Her father, physicist Russell Targ, cofounded the Stanford Research Institute to investigate psychic phenomena. Elisabeth participated in his ESP experiments, and he encouraged her to "remotely view" and predict her birthday presents before she opened them (and claims she was correct most of the time). Elisabeth Targ was an academic superstar. She graduated from high school at age 15, was fluent in Russian, German and French, and eventually graduated from Stanford Medical School

Targ and colleagues at California Pacific Medical Center in San Francisco published a double-blind study in the Western Journal of Medicine that rocketed her to fame in the field of complementary and alternative medicine: Forty healers around the U.S. were recruited to pray for the health of patients with advanced AIDS. The prayed-for group had significantly fewer opportunistic illnesses than the control group, and Targ instantly became the poster child for a fledgling new field exploring prayer and healing. "Elisabeth is our hero," wrote Mitchell Krucoff, a Duke University Medical Center cardiologist who has pioneered complementary therapies in patients with heart disease.

Targ's research was impressive enough that the National Institutes of Health gave her $1.5 million to carry out two more distant-prayer studies, one on AIDS and another on glioblastoma multiforme, an aggressive and almost inevitably fatal brain tumor. In Europe and the U.S. there are approximately two to three new cases per 100,000 people annually. "It is a particularly gnarly disease from which people rarely recover," says her father, "and that's why she wanted to study it."

Two months later, Targ, who was 40, began fertility treatments: she and her fiance, physicist Mark Comings, wanted a family. That spring, however, she began finding it difficult to pronounce words with the letter "b," and one morning the left side of her face sagged. A high-resolution MRI revealed that she was suffering from a rapidly growing grade 4 glioblastoma multiforme brain tumor. Word of the horrific diagnosis spread, and healers began calling, visiting and praying from a distance—in a truly eerie echo of her newly funded study. But they could not save her. Targ died at 11:11 p.m., 111 days after her diagnosis.

The coincidences, if we may call them that, did not end with Targ's death. Kate MacPherson, a healer and registered nurse in Salinas, California, had participated in Targ's first study on AIDS and prayer. "About a month after Elisabeth died," says MacPherson, "I had a dream."

In the dream, Comings (who married Targ shortly before her death) was sitting on a weathered wooden box in an old European town with cobbled streets and stone buildings. "He was devastated," recalls MacPherson, "and Elisabeth kept repeating something to him. I couldn't understand it. I thought maybe it was Hebrew. The sounds were ya vas liu bliu. I wrote down the dream and phonetics and sent it to Mark, whom I knew in passing."

Russell Targ recalls the Sunday morning when Comings came over to his home and read MacPherson's letter out loud. Targ instantly recognized the syllables as the Russian words for "I love you." Elisabeth was not only fluent in the language but had traveled there with her dad.

Yet another coincidence? "So many mystical things have happened to me in the aftermath of Elisabeth's death," says Comings, who to this day wears not only his wedding ring, but Elisabeth's as well. "The stories are mind-blowing, even to the parapsychologists who study these things for a living."

Lucky Accidents

One thing is certain about coincidence. The phenomenon fascinates believers and skeptics alike. It's a porthole into one of the most interesting philosophical questions we can ask: Are the events of our lives ultimately objective or subjective? Is there a deeper order, an overarching purpose to the universe? Or are we the lucky accidents of evolution, living our precious but brief lives in a fundamentally random world that has only the meaning we choose to give it?

For those with a highly empirical bent, a coincidence is happenstance, a simultaneous collision of two events that has no special significance and obeys the laws of probability. "In reality, the most astonishingly incredible coincidence imaginable would be the complete absence of all coincidence," says John Allen Paulos, professor of mathematics at Temple University in Philadelphia, and best-selling author of Innumeracy: Mathematical Illiteracy and Its Consequences. "Believing in the significance of oddities is self-aggrandizing," he adds. "It says, 'Look how important I am.' People find it dispiriting to hear, 'It just happened, and it doesn't mean anything.'"

To the mystically inclined, however, coincidence is a synchronicity, the purposeful occurrence of two seemingly unrelated events. The argument is not likely to be resolved anytime soon. Of late, though, the phenomenon of coincidence has begun to yield new scientific insights. It turns out that we may actually be hardwired to connect anomalies in a meaningful way. Many of the remarkable feats our brains regularly perform—including our ability to learn the meaning of words or decode the unspoken laws of social decorum depend on our penchant for noticing coincidences. In fact, mathematicians, cognitive scientists and paranormal researchers are applying the tools of statistics and probability to tease out just where coincidences lie on the bell curve of everyday experience. Are they easily explained, or so improbable they must signify something?

Comets, Dogs and Dalmatians

In A.D. 66 a comet was seen across the sky in Jerusalem just as the Jewish people were revolting against the Romans. In 1066, another comet appeared, just before the fateful Battle of Hastings was fought over the throne of England. Were these merely strange coincidences—or are comets portents of divine intent?

In 1705 English astronomer Edmund Halley was looking through old records of comets when he noticed a coincidence: The bright comets of 1531, 1607 and 1682 had almost the same orbits and appeared approximately every 75 years. Halley concluded they were one comet and predicted it would reappear in 1758. On Christmas night of 1758, Halley's comet appeared, forever changing our understanding of comets.

Indeed, coincidences help prod science along. "They are a true paradox," says MIT cognitive scientist Josh Tenenbaum. "On the one hand they seem to be the source of our greatest irrationalities—seeing causal connections when science tells us they aren't there. On the other hand, some of our greatest feats of scientific discovery depend on coincidences."

According to Tenenbaum, we could not learn language and syntax without the ability to notice strange coincidences. "Consider the challenge in learning just a single word," says Tenenbaum. "Every word is in a sense an infinite object. It's not just a name for an individual thing, it refers to an infinite set of things." Take the word "dog"—to understand that simple word you have to understand the name (Rover), the type (say, a black Labrador), all dogs, all mammals, all animals, all Labradors, all black Labradors (or black poodles, or black Great Danes), all running things, all furry things. "Yet even children under 5 can be given just a few relevant examples of dog and learn to use it," marvels Tenenbaum. Even more remarkable is that between the ages of 1 and 5, children are learning at least five new words a day.

Children make these cognitive leaps by noticing coincidences—Labradors and poodles and other dogs bark, pant with their tongues on hot days and, in cities at least, appear on leashes led by humans. Tenenbaum has demonstrated that we can generalize meaningfully from just a few examples of a novel word. In one study, 25 adults were shown sets of photographs (animals, vegetables, vehicles), and presented with a "novel" non-English word (such as "blick") as the name for the object. They were asked to point out instances of "blick" in additional photographs. Tenenbaum found that after seeing an object (such as a Dalmatian) with the name "blick" only once, adults were able to infer that the word either referred to all Dalmatians or all dogs. If they were shown three Dalmatians as three examples of "blick," they were much more likely to infer that "blick" referred only to Dalmatians. A pilot study found that even 4-year-old children could generalize properly if presented "blick" three times.

"Coincidences drive so many of the inferences our minds make," says Tenenbaum. "Our neural circuitry is set up to notice these anomalies and use them to drive new learning. There is an old saying that neurons that fire together wire together. So you could say that coincidence operates at the level of the synapse, whenever neurons fire at the same time." If our minds are primed to find coincidences, it's not surprising that we sometimes see connections where they don't exist. But do we fall into that trap too often?

It's Just a Coincidence!

"What are the odds of that?" asks SQuire Rushnell [sic] again and again in his best-selling book, When God Winks, an entertaining collection of confounding coincidences, from star-crossed lovers to holocaust survivors who were reunited years later. When Rushnell began writing the book, he was pondering the famous fact that John Adams and Thomas Jefferson, two men who shaped the Declaration of Independence, both died on July 4, 1826, the fiftieth anniversary of the signing of that historic document.

"I sat in my small study wondering whether there were more coincidences connecting the two men," recalls Rushnell. He pulled a reference book off his shelf, but it had no useful information. "Then I noticed a thin, homely, old volume right next to the reference book. I'd brought it back in a box of books after my grandfather's funeral and never noticed it before. It was a collection of Daniel Webster's speeches, and the first one was a eulogy for Adams and Jefferson." The speech described many coincidences linking the two men. In later research, Rushnell discovered that the book was available in only one public library in the Eastern U.S., the rare book section of the Library of Congress. "Yet here was a copy from my grandfather, sitting right there on my shelf, just when I needed it," exclaims Rushnell. "What are the odds of that?"

Not as small as you'd think, answer mathematicians who study the laws of probability. "In 10 years there are 5 million minutes," says Irving Jack Good, a professor in the department of statistics at Virginia Polytechnic Institute in Blacksburg. "That means each person has plenty of opportunity to have some remarkable coincidences in his life." Good recalls his own remarkable coincidence: He was at a conference listening to a speaker who described a mathematical proof, and later that day opened a mathematics textbook at random in the library. On the open page was a shorter proof of the same theorem. "I estimated that coincidence had a probability of 10^11."

Improbable occurrences are to be expected, say statisticians, especially considering there are 5 billion people on the planet. "We're awash in a torrent of names, numbers, dates, addresses, acronyms, telephone calls, e-mails, calendars, birth dates," says John Paulos. "The information-rich environment of modern life itself is a source of many coincidences." Even "prophetic" dreams can be explained by probability, says Paulos. This country dreams a half billion hours each night (250 million people dreaming two hours a night). Some of those dreams are bound to coincide with real events.

Mathematicians point out that people are notoriously inaccurate in predicting probability. We are, in a sense, mathematically naive. Perhaps one of the most famous experiments to demonstrate this is known as the "birthday problem." There are 365 days a year, and 366 in a leap year. To absolutely guarantee that two people in the same room share a birthday, you need 367 people. But how many people are needed to ensure a 50 percent chance of a shared birthday (such as July 4)? Most people guess about half of 366—or 183. The actual answer is surprisingly low: you need only 23 people. However, if you specify an exact birth date (July 4, 1976), you need 613 people to reach a 50 percent probability. The upshot: improbable events are quite likely to occur but specific, predicted improbable events are far less likely.

If we understood probability theory better, would we be less bewitched by coincidences? Perhaps not. Josh Tenenbaum says we're actually very good at inferring probabilities—as long as the data are presented in a way that reflects real-world thinking. "Asking people for an arbitrary number in terms of probability—such as 'What are the odds that three people share the same birthday?'—is asking them to perform a strange calculation," explains Tenenbaum. "But we are extremely good at noticing data that might have an underlying common cause." Tenenbaum and doctoral candidate Thomas Griffiths showed Stanford University undergraduates 14 sets of birth dates reflecting either randomness (such as 2, 4, 6 and 8 unrelated birthdays) or coincidence (such as 4 birthdays on the same day). The students were asked to rate how big a coincidence each set of birth dates was on a scale of 1 to 10. "There was a very high correlation between people's intuition about coincidence and the correct probability," says Tenenbaum, who suggests that if we change the way we model questions about probability we'll conclude that humans actually excel at detecting the singularity of an event.

The Other Side of Probability

We may be highly skilled at detecting and connecting anomalous events, but that doesn't help us understand events so spectacular that they are readily noticed—but not easily explained. "I have no argument with people who suggest that very unusual events happen every so often and have no intrinsic significance," says Dean Radin, author of The Conscious Universe: The Scientific Truth of Psychic Phenomena,and senior scientist at the Institute of Noetic Sciences in Petaluma, California, which studies psychic phenomena. "I just don't accept that this explanation is correct 100 percent of the time." For instance, in laboratory studies he's found that people seem to know when they're going to view upsetting photos. A measurement of electrical activity on their skin rises before viewing disturbing photos randomly selected by a computer. The same changes do not occur before neutral or calming photos appear. "Science makes assumptions about the way things work, and yet we still understand so little. I'm willing to dance with the mystery without requiring the whole answer ahead of time," says Radin.

Radin, who studies everything from precognition to remote viewing, tests coincidence on a global scale specifically, whether events with a worldwide impact focus consciousness and influence the functioning of machines. To study this, a volunteer collaboration of 75 researchers around the world joined in the Global Consciousness Project, headed up by Radin and psychologist Roger Nelson of Princeton University. The researchers are monitoring 75 devices called random number generators. These machines generate numbers based on electronic noise like the static you hear between radio stations. The goal is to measure whether events that focus mass consciousness tip the random number generators toward significantly greater randomness or significantly greater coherence.

On September 11, 2001, a few hours before the World Trade Center was attacked, there was a large, anomalous spike in the 37 generators being monitored at that time—a uniform rise in what statisticians call variance. In a sense the generators were extremely "noisy," says Radin. "Over the course of the rest of the day," the opposite happened. There was a drop in magnitude that was uncharacteristically quiet, and unique for that entire year." On March 11, 2004, after the terror attacks in Madrid, it was also unusually "noisy," but the next day, during the demonstrations in Spain, there was once again uncharacteristic coherence, or "quiet." Disasters disrupt global consciousness (and the machines), hypothesizes Radin, while mass demonstrations and celebrations lead to a coherent mind field, which shifts these supposedly random machines toward more coherence and "quiet."

What does this have to do with coincidence—besides that the data itself might be a mere coincidence? Computer scientist Richard Shoup, president of the Boundary Institute in Saratoga, California, which studies psychic phenomena, thinks this kind of data may challenge the assumption of fundamental randomness that is at the core of theories like quantum mechanics—and thereby challenge the worldview of those who chalk up coincidences to happenstance. Shoup wonders if other sources of random data on September 11, such as devices that were scanning the radio spectrum for signals, also showed a shift. "The data seem to show that observation can change things, that maybe thoughts affect the world," says Shoup. "We need more people to think about this." One person who is thinking deeply about this is Mark Comings. A week after Elisabeth Targ died, he happened to be at a bank around the corner from the place in Palo Alto, California, where they'd had their first dinner. The site is now a Border's Books store, but the courtyard and tables where they ate are still there. "I was filled with emotion remembering our meeting so long ago and thinking what a profound impact she'd had on my life," recalls Comings. "Then all of a sudden I heard her voice in my head, saying, 'Get that book.' I turned around and at that moment a person was pushing a cart of books by me, and on the cart was a cardboard sign with a hand pointing down that read, 'This one is for you.' I walked over to the book it was pointing at. It was called The Field: The Quest for the Secret Force of the Universe. I picked it up and opened to a footnote about Elisabeth and a famous remote viewing experiment she'd done." It turned out there was an entire chapter about Elisabeth Targ, so Comings bought the book, and brought it to Russell Targ. "He hadn't seen it. It was a new book that had just been published."

Comings finds solace in his view of the universe, which embraces the import of coincidences. "I have a sense of real and dynamic interaction between [me and Elisabeth]. But I have a unique view of the world," he says.

He also finds comfort in Targ's enduring legacy. One hundred fifty patients with glioblastomas are enrolled in the study she devised before succumbing to the cancer.